
/* 
 *  M_APM  -  mapmcbrt.c
 *
 *  Copyright (C) 2000 - 2007   Michael C. Ring
 *
 *  Permission to use, copy, and distribute this software and its
 *  documentation for any purpose with or without fee is hereby granted,
 *  provided that the above copyright notice appear in all copies and
 *  that both that copyright notice and this permission notice appear
 *  in supporting documentation.
 *
 *  Permission to modify the software is granted. Permission to distribute
 *  the modified code is granted. Modifications are to be distributed by
 *  using the file 'license.txt' as a template to modify the file header.
 *  'license.txt' is available in the official MAPM distribution.
 *
 *  This software is provided "as is" without express or implied warranty.
 */

/*
 *      $Id: mapmcbrt.c,v 1.8 2007/12/03 01:50:32 mike Exp $
 *
 *      This file contains the CBRT (cube root) function.
 *
 *      $Log: mapmcbrt.c,v $
 *      Revision 1.8  2007/12/03 01:50:32  mike
 *      Update license
 *
 *      Revision 1.7  2003/05/05 18:17:38  mike
 *      simplify some logic
 *
 *      Revision 1.6  2003/04/16 16:55:58  mike
 *      use new faster algorithm which finds 1 / cbrt(N)
 *
 *      Revision 1.5  2002/11/03 21:34:34  mike
 *      Updated function parameters to use the modern style
 *
 *      Revision 1.4  2000/10/30 16:42:22  mike
 *      minor speed optimization
 *
 *      Revision 1.3  2000/07/11 18:03:39  mike
 *      make better estimate for initial precision
 *
 *      Revision 1.2  2000/04/08 18:34:35  mike
 *      added some more comments
 *
 *      Revision 1.1  2000/04/03 17:58:04  mike
 *      Initial revision
 */

#include "m_apm_lc.h"

/****************************************************************************/
void	m_apm_cbrt(M_APM rr, int places, M_APM aa)
{
M_APM   last_x, guess, tmpN, tmp7, tmp8, tmp9;
int	ii, nexp, bflag, tolerance, maxp, local_precision;

/* result is 0 if input is 0 */

if (aa->m_apm_sign == 0)
  {
   M_set_to_zero(rr);
   return;
  }

last_x = M_get_stack_var();
guess  = M_get_stack_var();
tmpN   = M_get_stack_var();
tmp7   = M_get_stack_var();
tmp8   = M_get_stack_var();
tmp9   = M_get_stack_var();

/* compute the cube root of the positive number, we'll fix the sign later */

m_apm_absolute_value(tmpN, aa);

/* 
    normalize the input number (make the exponent near 0) so
    the 'guess' function will not over/under flow on large
    magnitude exponents.
*/

nexp = aa->m_apm_exponent / 3;
tmpN->m_apm_exponent -= 3 * nexp;

M_get_cbrt_guess(guess, tmpN);

tolerance       = places + 4;
maxp            = places + 16;
bflag           = FALSE;
local_precision = 14;

m_apm_negate(last_x, MM_Ten);

/*   Use the following iteration to calculate 1 / cbrt(N) :

                                 4
         X     =  [ 4 * X - N * X ] / 3
          n+1   
*/

ii = 0;

while (TRUE)
  {
   m_apm_multiply(tmp8, guess, guess);
   m_apm_multiply(tmp7, tmp8, tmp8);
   m_apm_round(tmp8, local_precision, tmp7);
   m_apm_multiply(tmp9, tmpN, tmp8);

   m_apm_multiply(tmp8, MM_Four, guess);
   m_apm_subtract(tmp7, tmp8, tmp9);
   m_apm_divide(guess, local_precision, tmp7, MM_Three);

   if (bflag)
     break;

   /* force at least 2 iterations so 'last_x' has valid data */

   if (ii != 0)
     {
      m_apm_subtract(tmp8, guess, last_x);

      if (tmp8->m_apm_sign == 0)
        break;

      if ((-4 * tmp8->m_apm_exponent) > tolerance)
        bflag = TRUE;
     }

   local_precision *= 2;

   if (local_precision > maxp)
     local_precision = maxp;
  
   m_apm_copy(last_x, guess);
   ii = 1;
  }

/* final cbrt = N * guess ^ 2 */

m_apm_multiply(tmp9, guess, guess);
m_apm_multiply(tmp8, tmp9, tmpN);
m_apm_round(rr, places, tmp8);

rr->m_apm_exponent += nexp;
rr->m_apm_sign = aa->m_apm_sign;
M_restore_stack(6);
}
/****************************************************************************/

